It insinuates it's overpowered, yet it says that Pyro being able to get free Melee kills in pubs... balances it?

If anything that would be an arguing point for it being balanced in pubs, underpowered outside of it. Large health penalties isn't the solution either since the whole point of the powerjack is that rather than having direct kill power you kill with it to stay healthy, low HP counteracts half of the set if anything.

Heal Flame Thrower (just fix the particles so that they can actually hit things when you have more than a hundred ping >.>)

Hurt Pistol

And Utilt, I'm not entirely certain, but I think it might be pertaining to Gas Jockey's speed vs. its bullet vulnerability. In pubs the Pyro can get away with meleeing people more easily, and though he can't do so in a comp setting, the bullet vulnerability gives little reason to not want a 10% speed boost. It's basically free speed, I'm guessing.

Though I could be completely off-base. I'm not sure how the mention of the Powerjack plays into the OP's explanation?